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## Soccer Scores - Answer

The numbers of goals scored by the 11 players were 5, 7, 11, 13, 17, 19, 29, 31, 37, 41 and 43.

There are 14 primes which are less than 45, the eleven from the correct answer plus 2, 3, and 23. The sum of all 14 = 281. The sum of the smallest 11 = 160. The sum of the largest 11 = 271.

Let A = the average score of the 11 players. Then A must be a prime between 14.5 and 24.6 which could be 17, 19 or 23.

Let S = the sum of two primes which are not used as one of the 11 scores or the average score. Then S = 281 - 11A - A = 281 - 12A.

If we substitute the three possible values for A we get S = 77, 51 or 5. So the only solution is S = 2 + 3 and A = 23. The average score is 23.

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